Bayesial network

P(M|B)=P(M^B)
P(B)
=∑P(M B e a j)
∑P(m B e a j)
∑ P(MΛBΛeΛaΛj):
1) P(MΛBΛEΛAΛJ)=P(M|A) ×P(B) ×P(E) ×P(J|A) ×P(A|BΛE)
=0.70×0.001×0.002×0.90×0.95
=1.197×10-6
2) P(MΛBΛ EΛAΛJ)=P(M|A) ×P(B) ×P( E) ×P(J|A) ×P(A|BΛ E)
=0.70×0.001×0.998×0.9×0.94
=5.910156×10-4
3) P(MΛBΛEΛ AΛJ)=P(M| A) ×P(B) ×P(E) ×P(J| A) ×P( A|BΛE)
=0.01×0.001×0.002×0.05×0.05
=5×10-11
4) P(MΛBΛEΛAΛ J)=P(M|A) ×P(B) ×P(E) ×P( J|A) ×P(A|BΛE)
=0.70×0.001×0.002×0.1×0.95
=1.33×10-7
5) P(MΛBΛ EΛAΛ J)=P(M|A) ×P(B) ×P( E) ×P( J|A) ×P(A|BΛ E)
=0.70×0.001×0.998×0.1×0.94
=6.56684×10-5
6) P(MΛBΛEΛ AΛ J)=P(M| A) ×P(B) ×P(E) ×P( J| A) ×P( A|BΛE)
=0.01×0.001×0.002×0.95×0.05
=9.5×10-10
7) P(MΛBΛ EΛ AΛJ)=P(M| A) ×P(B) ×P( E) ×P(J| A) ×P( A|BΛ E)
=0.01×0.001×0.998×0.05×0.06
=2.994×10-8
8) P(MΛBΛ EΛ AΛ J)=P(M| A) ×P(B) ×P( E) ×P( J| A) ×P( A|BΛ E)
=0.01×0.001×0.998×0.95×0.06
=5.6886×10-7
Sum=6.5861326×10-4


P(B)=P(jΛBΛeΛaΛm)
1) P(JΛBΛEΛAΛM)=P(J|A) ×P(B) ×P(E) ×P(M|A) ×P(A|BΛE)
=0.9×0.001×0.002×0.70×0.95
=1.197×10-6
2) P(JΛBΛ EΛAΛM)=P(J|A) ×P(B) ×P( E) ×P(M|A) ×P(A|BΛ E)
=0.90×0.001×0.998×0.70×0.94
=5.9101×10-4
3) P(JΛBΛEΛ AΛM)= P(J| A) ×P(B) ×P(E) ×P(M| A) ×P( A|BΛE)
= = 5×10-11
4) P(JΛBΛEΛAΛ M)= P(J|A) ×P(B) ×P(E) ×P( M|A) ×P(A|BΛE)
= 0.90×0.001×0.002×0.30×0.95
= 5.13×10-7
5) P(JΛBΛ EΛAΛ M)=P(J|A) ×P(B) ×P( E) ×P( M|A) ×P(A|BΛ E)
=0.90×0.001×0.998×0.30×0.94
=2.532924×10-4
6) P(JΛBΛEΛ AΛ M)=P(J| A) ×P(B) ×P(E) ×P( M| A) ×P( A|BΛE)
=0.05×0.001×0.002×0.99×0.05
=4.95×10-9
7) P(JΛBΛ EΛ AΛM)=P(J| A) ×P(B) ×P( E) ×P(M| A) ×P( A|BΛ E)
=0.05×0.001×0.998×0.01×0.06
=2.994×10-8
8) P(JΛBΛ EΛ AΛ M)=P(J| A) ×P(B) ×P( E) ×P( M| A) ×P( A|BΛ E)
=0.05×0.001×0.998×0.99×0.06
=2.96406×10-6
9) P( JΛBΛEΛAΛM)=P( J|A) ×P(B) ×P(E) ×P(M|A) ×P(A|BΛE)
=0.10×0.001×0.002×0.70×0.95
=1.33×10-7
10) P( JΛBΛ EΛAΛM)=P( J|A) ×P(B) ×P( E) ×P(M|A) ×P(A|BΛ E)
=0.10×0.001×0.998×0.7×0.94
=6.56684×10-5
11) P( JΛBΛ EΛ AΛM)=P( J| A) ×P(B) ×P( E) ×P(M| A) ×P( A|BΛ E)
=0.95×0.001×0.998×0.01×0.06
=5.586×10-7
12) P( JΛBΛ EΛ AΛ M)=P( J| A) ×P(B) ×P( E) ×P( M| A) ×P( A|BΛ E)
=0.95×0.001×0.998×0.99×0.06
=5.6317×10-5
13) P( JΛBΛEΛ AΛM)=P( J| A) ×P(B) ×P(E) ×P(M| A) ×P( A|BΛE)
=0.95×0.001×0.002×0.01×0.05
=9.5×10-10
14) P( JΛBΛEΛ AΛ M)=P( J| A) ×P(B) ×P(E) ×P( M| A) ×P( A|BΛE)
=0.95×0.001×0.002×0.99×0.05
=9.405×10-8
15) P( JΛBΛEΛAΛ M)= P( J|A) ×P(B) ×P(E) ×P( M|A) ×P(A|BΛE)
= 0.10×0.001×0.002×0.30×0.95
= 5.7×10-8
16) P( JΛBΛ EΛAΛ M)=P( J|A) ×P(B) ×P( E) ×P( M|A) ×P(A|BΛ E)
=0.10×0.001×0.998×0.30×0.94
=2.81436×10-5

Sum=9.9998346×10-4
≈0.001

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P(M|B)=P(M^B)
P(B)
=∑P(M B e a j)
∑P(m B e a j)
= 6.5861326×10-4
0.001
=0.6586
=0.66

so, the probability for Mary to make call when there is Burgary is 0.66.
However, the probability for Jonh to make a call when there is burgary is 0.84
So, we can conclude that John is more reliable to make a call when there is burgary.